g(x) 6. Let's mix things up. Consider lim 1+00 E(x) I don't have any algebraic tricks for you this time, so let's investigate this numerically. Calculate this ratio for r 5, x = 10, and a = 50.

Q: lim (e +x)/* 1/x

A: The solution is given as

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A:

Q: lim as x approaches 4 from the right of 8-2x/|x2-x-12| a. 2  b.-2  c. -1  d. 4  e. infinity

A: The given expression is,

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A:

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A: Given: limy→01+xsin1x1+xcos1x

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A: the objective is to find the derivative of the given function by using definition of derivative

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A: Note: We are entitled to solve only one question at a time. To Find: i. limy→01+xsin1x1+xcos1xii.…

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A:

Q: b) Find two functions such that lim, 0 f(x) = 0 lim, 0 g(x) = 0 but lim, 0 f(x)g(x) = 1

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Q: Determine whether the statement makes sense or does not make sense, and explain your reasoning.

A: Let us consider limx→a-f(x)=A and limx→a+f(x)=B We have, A is not equal to B. When x gets close to…

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A:

Q: :. Solve. (a) For 2x + 5 if x 5 find lim g(x), lim g(x), and lim g(x). I+5+

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Q: 3 k3 -ル+} (my)0, t) 4 +n -y lim

A: Given that  Limit

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A: We have to find limx→∞ e4x-7e2x1-e4x.

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A:

Q: f(x)- x3-3y 4 t 3x 315 x²† 10x 4+3x315 x†10x lim カー70 Derivation of

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Q: X'+2X Lim メーロ 0 @ True eflase laşe 8.

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A: Given:  limx→∞-x2-2x-4x2+x-20

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A: To compute the following limit

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A:

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A:

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A: Given,           limx→∞ex+x1x

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A:

Q: The concentration of a drug in an organ at any time t (in seconds) is given by x(t) = 0.08 + 0.12(1…

A: To find the initial concentration of the drug

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A: To evaluate the given limit: lim(x,y)→(1,0)y2+6xy3x-y-3 along the path x=ey. Here,…

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A: Given limit is : limx→2∫10x2+3xt-1etdt2x-4dt To find the value of limit by using L’Hospital’s.

Q: (M1.4 C) Consider the two functions h(x) = %3D and k(x) 2² + 4x+4 2+x-2 Compute the lim h(x) and lim…

A: Given: The functions hx=x2+x-2x2+4x+4 and kx=x2+4x+4x2+x-2 To find: limx→-2hx and limx→-2kx

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A: For x->5^+ , x-5 -> 0^+So denominator equals to 0.We can not find the limit by plugging the…

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A:

Q: The graph of f(x) passes through the point (4, 0). The slope of the line tangent to the graph at the…

A:

Q: xsinx lim x→0 e*+e¯x-2cosx

A: Since, we have been given up the expression:-limx→0 x sin (x)ex+e-x-2 cos (x)-(i)Since,on applying…

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A:

Q: 2. メー gu)= - fex) = X üls Is1 3メ-1 احب lim (fog) x メー

A: We have to find limit

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A: we have to find the limit

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A:

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A:

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A: Given limit, limx→12xx-1x-1

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A:

Q: b. lim X-0* e -3/x 2 X²

A: Please see the attachment

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A:

Q: V4 - x2 0sx<2 lim f(x), where f(x) = < 2 9) x-4" 2 sx<4 x = 4 B) Does not exist A) 4 C) 2 D) 0

A: f(x)=4-x20≤x&lt;222≤x&lt;44x=4

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A:

Q: 4x? — 25х + 25 (a) lim x→5 x² – 8x + 15 | Vx + 22 – 5 (b) lim x→3 x – 3 -

A: The limit of a function limx→Xfx=Y means that value of  function fx can be as close to Y by making…

Q: 2 ] (d) lim x-1Lx-1 x2 -1

A: Topic = Limits

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A: Explanation of the answer is as follows

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A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: